Topics within Exponents & More
Exponents are a way of writing repeated multiplication. For example, let's consider this expression:
$$3+3+3+3+3+3$$
Not very pretty, is it? You (should have) learned that this can also be written as
$$3\cdot6$$
which is 3 added to itself 6 times. Similarly, if we have an expression like this:
$$3\cdot3\cdot3\cdot3\cdot3\cdot3$$
We can write it using an exponent as
$$3^6$$
(read as 3 to the power of 6, 3 to the 6th power, or 3 to the 6th).
In this example, the "3" is called the base, and it is the number being multiplied by itself. The "6" is called the exponent, and it is the number of times that the base is multiplied by itself. This notation is called exponential form. A base together with its exponent are called a power.
To type a power on a computer, type {base}^{exponent}. For example, for $3^6$ we would type 3^6.
Your turn! Write the following in exponential form:
$\displaystyle{2\cdot2\cdot2\cdot2}=$
What is exponential form?
Which number is the base? How about the exponent?
2 is the base, and 4 is the exponent. In exponential form, this is $2^4$.